Understanding the blood alcohol (BAC) calculator — concept and principle
This calculator gives a rough estimate of blood alcohol concentration (BAC) with the Widmark formula, from sex, body weight, the drinks consumed and the time since the first drink. It also shows the peak value, grams of pure alcohol, standard drinks and units, and the hours until BAC falls below common legal limits. It is meant for education about how alcohol accumulates and clears, not for deciding whether to drive.
How it is calculated
- Pure alcohol (g) = drinks × volume (mL) × ABV × 0.789 g/mL
- Peak BAC (%) = alcohol (g) ÷ (body weight (g) × r) × 100, with r = 0.68 for men and 0.55 for women
- BAC now = peak − 0.015 × hours since the first drink
- Hours until a level = (BAC now − level) ÷ 0.015
- US standard drinks = g ÷ 14; UK units = g ÷ 8
The principle
Erik Widmark showed that alcohol spreads through the body's water, so the same amount gives a higher concentration in a smaller body or one with less water. The factor r represents that share of body weight; women on average have less body water per kilogram. The liver then removes alcohol at a roughly constant rate, typically about 0.015% per hour, though real rates range from about 0.010 to 0.025. Food, medication, health and drinking speed all change the real curve.
Worked example
Defaults: man, 70 kg, 3 drinks of 355 mL at 5%, 2 hours since the first drink.
- Alcohol = 3 × 355 × 0.05 × 0.789 = 42 g = 3 US standard drinks = 5.3 UK units.
- Peak = 42.01 ÷ (70,000 × 0.68) × 100 = 0.088%.
- Now = 0.088 − 0.015 × 2 = 0.058% = 0.58 ‰.
- Hours until about 0.00% = 0.058 ÷ 0.015 = 3.9; below 0.03% = 1.9; below 0.05% = 0.6; below 0.08% = 0.
| Body weight (kg) | Estimated BAC now (%) |
|---|---|
| 17.5 | 0.323 |
| 35 | 0.147 |
| 52.5 | 0.088 |
| 70 | 0.058 |
| 87.5 | 0.041 |
| 105 | 0.029 |
| 140 | 0.014 |
How to read the result
The estimate is for a population average and can be wrong by a wide margin for any individual. An estimate below the legal limit does not mean you are safe to drive: impairment starts at low levels, and limits differ by country, for example 0.03% in Korea and 0.08% in the US and England and Wales. The only safe choice is not to drive after drinking.
Common mistakes
- Using the result to decide whether to drive.
- Assuming coffee, a shower or sleep speeds up elimination.
- Forgetting that drinks with food absorb more slowly but still count.
- Underestimating pour sizes and ABV.
Frequently asked questions
How long does it take for alcohol to leave the body?
On average BAC falls about 0.015% per hour, but rates vary between people.
What is the legal limit in Korea?
0.03% BAC for driving under the Road Traffic Act.
Why do women reach higher BAC?
On average they have a smaller share of body water, so the same alcohol is more concentrated.
Sources: Washington State Patrol breath-test training material, "Widmark's Equation" (2002) · NIAAA, standard drink of 14 g; NHS, UK unit of 8 g · Korea Road Traffic Act, Article 44